Numerical Solutions of Nonlinear Radiative Heat Transfer Problems for Boundary Layer Flows

Abstract

Boundary layer ows subject to heat transfer have enormous industrial and engineering applications such as heat treatment of material travelling between a feed roll and wind-up roll, cooling of large metallic plates, cooling towers, solar water heating, distribution of moisture over groove elds, die forging, condensation processes, polymer extrusion and many others. In particular the radiative heat transfer is important in solar power technology, combustion applications such as re, furnaces, IC engines, chemical engineering processes, various propulsion devices for aircrafts, missiles, satellites and space vehicles etc. A literature survey witnesses that boundary layer ow problems with linear Rosseland heat ux has been signi cantly addressed. This dissertation investigates some fundamental ow problems with the consideration of non-linear radiative heat transfer. Salient features a ecting such ows have also been addressed. These include magnetic eld, buoyancy forces, convective boundary, Brownian motion and thermophoretic diffusion due to nanoparticles, viscoelasticity, viscous dissipation and Joule heating. The developed di erential system has been treated numerically through well known shooting method with fth order Runge-Kutta integration. Numerical solutions through MATLAB builtin routine bvp4c are also presented in some cases. Chapter 1 includes a detailed background of the boundary layer ows over moving or stationary surfaces and boundary layer ows of non-Newtonian uids and nano uids. Moreover, two-dimensional boundary layer equations for generalized Newtonian (powerlaw and Eyring-Powell uids), viscoelastic uids and nano uids have been presented. Finally the numerical approach used in this dissertation is elaborated. In Chapter 2, we emphasize the e ects of nonlinear radiative heat transfer on the ow of Powell-Eyring uid induced by a non-linearly stretching sheet. The arising non-linear problem is dealt numerically. In uences of parameters especially the radiation parameter on the ow elds are discussed. The main frame work of this chapter is submitted for publication in Open Physics. Chapter 3 describes the ow of upper-convected Maxwell (UCM) uid a ected by non-linear radiation heat transfer. UCM uid is bounded by an isothermal stretching wall. Numerical solutions through both the shooting method and collocation method based MATLAB package bvp4c are evaluated. Comparison of the present computations with the previously reported results is also seen. The main ndings of this chapter have been published in Journal of Aerospace Engineering 27 (2014) 04014015. doi:10.1061/(ASCE)AS.1943-5525.0000361. Stagnation-point ow of power-law uid with nonlinear radiative heat transfer is discussed in Chapter 4. The problem is rst formulated and then investigated numerically for several values of embedded parameters. Power-law uids of both shear-thinning and shear-thickening nature have been studied. The contents of this chapter have been published in International Journal of Numerical Methods for Heat & Fluid Flow 25 (2015). doi:10.1108.2FHFF-05-2014-0147. Natural convective boundary layer ow of nano uid with non-linear radiative heat ux is considered in chapter 5. The e ects of magnetic eld, Joule heating and viscous dissipation are also incorporated. Numerical solutions are discussed with the variation of interesting parameters. The main ideas of this study have been published in PLoS ONE 9 (2014) e103946. doi:10.1371/journal.pone.0103946 Two-dimensional ow of a nano uid over a convectively heated radiative surface is described in chapter 6. Interesting aspects of Joule heating, viscous dissipation and magnetic eld are also considered. Buongiorno's model for nano uids is utilized in the formulation. At the end, the impact of physical parameters on the elds is sketched and analyzed. The main observations of this study are published in Journal of the Taiwan Institute of Chemical Engineers 45 (2014) 1176-1183. doi:10.1016/j.jtice.2013.11.008 In chapter 7, the non-linear radiative heat transfer analysis has been done for a moving electrically conducting uid over a stationary or moving at plate. Blasius and Sakiadis ow problems are obtained as special cases of this study. The numerical method is also able to simulate the model for both large and small values of the parameters. The graphical results are obtained for several values of the parameters. The key results of this chapter have been accepted for publication in International Journal of Numerical Methods for Heat & Fluid Flow. Non-linear thermal radiation is introduced for three-dimensional ow over a bidirectional stretching surface in chapter 8. The two-dimensional and axisymmetric ow cases are shown to be special cases for the model. Graphical illustrations showing the e ect of parameters on the velocity, temperature, wall shear stress and wall heat transfer rate are presented and discussed. The obtained numerical solutions are found in excellent agreement with the available studies. The results of this chapter are published in Zeitschrift Fur Naturforschung A 69 (2014) 705-713. doi:10.5560/zna.2014-0059 Chapter 9 extends the idea of chapter 8 for an exponentially stretching surface. The exponential surface temperature distribution is considered for numerical simulations. Graphs for velocity and temperature functions are prepared and discussed. The computational results for wall shear stress and wall heat transfer rate are obtained. The contents of this chapter have been published in Journal of the Taiwan Institute of Chemical Engineers 47 (2015) 43-49. doi:10.1016/j.jtice.2014. 10.011.